Questions tagged [kerr-metric]

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What happens when two ergospheres of oppositely spinning black holes of the same mass, axis of rotation, and speed of rotation approach?

What happens when two ergospheres of oppositely spinning black holes of the same mass, axis of rotation, and speed of rotation approach each other? What would happen to the black holes in question?
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How to show if a world line is null for a particular metric [closed]

For the Kerr metric, with line element $$ ds^2 = -\frac{\Delta-a^2\sin^2\theta}{\rho^2}dt^2 - \frac{4Mar\sin^2\theta}{\rho^2}dtd\phi +\frac{(r^2+a^2)^2-a^2\Delta\sin^2\theta}{\rho^2}\sin^2\theta d\phi^...
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Doubt on the precise definition of a general stationary rotating metric: the metric coefficients have which form?

Considering the following metric tensor $[1]$, with signature $(-,+,+,+)$, coordinates $(x^{0},x^{1},x^{2},x^{3})\equiv (t,r,\theta,\phi)$ and $c=1$: $$ds^{2} = g_{00}dt^{2} + g_{11}dr^{2} + g_{22}d\...
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Gravitational Redshift in Kerr Spacetime

Well, suppose then Schwarschild black holes. Following the $[1]$, we have the redshift factor: $$d\tau = \sqrt{1-\frac{2M}{r}}dt. \tag{1}$$ This factor have an physical interpretation to be the ...
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Spin rotation of masses in a rotating gravitational field around a black hole

If a rotational gravitational field affects masses in the way the frame and body velocities are added together does it mean that as the rotation of the frame has a gradient of the perpendicular ...
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51 views

Science of Kerr Black holes, can naked singularity form? Does it lead to another universe?

In the science fiction series, XeeLee Sequence, Stephen Baxter had used quite a lot of accurate physics in this hard science fiction. I was able to follow and determined which ones are true of our ...
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Horizons and other special surfaces on Kerr metric

The Kerr metric is \begin{equation} ds^2 = - \big(1-\frac{2GMr}{\rho^2}\big)dt^2-\frac{2GMra}{\rho^2}\sin^2 \theta \big(dtd\phi+d\phi dt\big)+ \frac{\rho^2}{\Delta}dr^2+\rho^2 d\theta^2 + \frac{\sin^...
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Trying to determine physically meaningful initial conditions for test particle around a Kerr black hole

I am working on some code for a test particle orbiting a Kerr black hole. I am trying to determine what the initial $ \frac{d t}{d\tau} $ would be. On Wikipedia https://en.wikipedia.org/wiki/...
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Symmetries of quasinormal modes of Kerr black hole

I have been reading this following paper on numerical evolution of the Teukolsky equation (see e.g. Eq 1 in their paper) for spin -2 fields about a spinning black hole (Kerr) solution. As the ...
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Gravitational waves from collapsing rotating mass? [closed]

According to the Birkhoff’s theorem, a non-rotating mass does not radiate gravitational waves during a spherically symmetric collapse. There is, however, no equivalent of the Birkhoff’s theorem for a ...
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Why do angular velocity deviates from Keplerian value close to a black hole?

The energy-momentum conservation equation in General Relativity is expressed as $T^{\mu\nu}_{\;\;;\nu}=0$ and by projecting this equation into the space normal to the four-velocity, we obtain the ...
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Does matter take infinite time to leave a black hole?

To this question: Can a sufficiently large black hole be singularity-free? about the possibility of a sufficiently large black hole not containing a singularity John Rennie posted an answer ...
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Some doubts regarding the effective potential for Kerr geometry

In the review Foundations of Black Hole Accretion Disk Theory, the authors defines an effective potential for Kerr geometry as (Chap. 2, eqn. 23) $$\Phi_{eff}=-\frac{1}{2}\ln\left|g^{tt}-2lg^{t\phi}+l^...
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Anatomy of a black hole: which are its layers?

I'm trying to find out how a Kerr-type black hole is structured (that is, a black hole with non-zero angular momentum but no net electrical charge). According to the information I have found, the ...
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What is the volume inside the inner event horizon of a Kerr black hole?

(Dokuchaev 2011) found periodic orbits of particles and photons inside a Kerr-Newman black hole with a maximally extended global geometry. They orbit inside the inner horizon $r<r_-$ where the $r$ ...
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What is the radius of the ringlike singularity of a Kerr BH?

For a rotating (Kerr) Black Hole the radius of the ring singularity is evaluated mathematically as R = a, see Metric diameter of a ring singularity. This means that R is always greater (or equal) to ...
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Where is the singularity located in a Kerr black hole?

In a rotating Kerr black hole is the ringlike singularity situated between the inner and the outer event horizon of the black hole?
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The physical interpretation of the trip inside Kerr (black hole) spacetime

Consider then the Kerr metric$[1]$: $$ds^{2} = -\Bigg(1-\frac{2Mr}{\rho^2}\Bigg)dt^2 - \frac{2Marsin^2(\theta)}{\rho^2}[dt d\phi+d\phi dt] +$$ $$+\frac{\rho^2}{\Delta}dr^2+\rho^2d\theta^2+ \frac{sin^...
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Time Derivative defined by Fermi transport in Kerr Space-Time

I have been studying 3+1 GR the last weeks. I have tried to comprehend Electrodynamics in curved space-time: 3+1 formulation (1982) Thorne McDonald I have studied another 3+1 GR book but it didn'...
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Normal vectors and induced metric Kerr metric

Consider the Kerr metric given by: $$ds^2 = -(1-\frac{2GMr}{\rho^2})dt^2 - \frac{2GMar\sin^2{\theta}}{\rho^2}(dtd\phi+d\phi dt)+ \frac{\rho^2}{\Delta}dr^2+\rho^2d\theta^2+ \frac{\sin^2\theta}{\rho^2}[...
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Particle falling into a Kerr black hole

Let's say that a particle starts a radial free fall towards a Kerr black hole with zero initial energy at $r\rightarrow\infty$. The initial angular momentum of the particle is zero ($p_\phi = 0)$. ...
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River model of a Kerr black hole: What does it mean for the spatial metric to be sheared?

I am currently trying to understand the river model for a Kerr black hole. There is one concept I don't grasp yet. What does it mean for the spatial metric to be sheared in the given context. I am ...
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Teukolsky-Starobinsky identities

The Teukolsky-Starobinsky identites relate solutions of the two Newman-Penrose scalars $\Psi_0$ and $\Psi_4$ around Kerr black holes. For example (here I am quoting Theorem 1 in Sec 81 of ...
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Is the Kerr metric more symmetric than a normal type D spacetime?

The Kerr spacetime is of Petrov type D (see here for the Petrov classification of spacetimes). In the Newman-Penrose formalism, from the Goldberg-Sachs theorem we can conclude that there is a choice ...
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Derivation of Teukolsky equation

I have been trying to derive the Teukolsky equation via the Newman-Penrose formalism. I have derived the following formula (see Eq. (2.14) in Teukolsky's paper) \begin{equation} (*) \left[(\Delta +3\...
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ZAMO's trajectory near a Kerr Black Hole?

sorry for the "generic" question, just that the last month I have been studying GR from 0 and having problems understanding some of the concepts. Anyways, to the question I wanted to ask: From my ...
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Effective potential for Kerr geometry

In the review Foundations of Black Hole Accretion Disk Theory, the authors defines an effective potential for Kerr geometry as (Chap. 2, eqn. 23) $$\mathcal{U}_{eff}=-\frac{1}{2}\ln\left|g^{tt}-2lg^{t\...
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1answer
166 views

What is exactly rotating in a rotating black hole?

I have read this: https://arxiv.org/abs/gr-qc/9404041 In General Relativity the black hole solutions which have so far been found form a four parameter family called the generalized Kerr-...
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How to derive the angular velocity of circular orbits in Kerr geometry?

I am trying to derive the angular velocity of a circular orbit in Kerr geometry, eqn.(2.16) in Bardeen et al (1972) which reads $$\Omega=\dfrac{1}{r^{3/2}+a}$$ (Note that I am using the units in which ...
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Derivation of radial momentum equation in Kerr geometry

I am trying to derive the radial momentum equation in the equatorial plane of Kerr geometry obtained by Lasota (1994) which reads (eqn. 6 in page-343; I am using units in which $M=1$) as follows: $$uu'...
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Physical significance of angular velocity of orbits around Kerr black holes

For the Kerr metric $$ds^2=\left(g_{tt}-\frac{g_{t\phi}^2}{g_{\phi\phi}}\right)dt^2+g_{\phi\phi}\left(d\phi-\omega dt\right)^2+g_{rr}dr^2+g_{\theta\theta}d\theta^2$$ the angular momentum is defined as ...
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Zero mass Kerr metric

When mass in Kerr metric is put to zero we have $$ds^{2}=-dt^{2}+\frac{r^{2}+a^{2}\cos^{2}\theta}{r^{2}+a^{2}}dr^{2}+\left(r^{2}+a^{2}\cos^{2}\theta\right)d\theta^{2}+\left(r^{2}+a^{2}\right)\sin^{2}\...
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Metric for a rotating star

If we want to describe a static spherically symmetric star we can use a metric which matches the Schwarzschild solution with correct mass on the outside of the star but differs from Schwartzschild in ...
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Light-like normal vectors

Can someone please show me how to mathematically establish that the normal vector to the event horizon of a Kerr Black Hole is light-like?
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171 views

Numerical Solutions for Equatorial Orbits in the Kerr Black Hole

Currently, I am trying to find timelike orbits in the Kerr metric around the equator. The problem is that no matter which parameters I choose or the method I use I can't seem to get to physically ...
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How to compute Kerr geodesics?

How would I start to numerically compute trajectories of Kerr geodesics with constants of motion like in this wikipedia page. I want to recreate trajectories like in this picture in Matlab.
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How does the Penrose diagram for a spinning black hole differ in realistic scenarios (formed by stellar collapse)?

The Penrose diagram for a non-spinning Schwarzschild black hole is Notably, there is a second universe "on the other side" of the black hole. However, actual black holes form by stellar collapse, and ...
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Metric diameter of a ring singularity

In the Kerr metric the ring singularity is located at the coordinate radius $r=0$, which corresponds to a ring with the cartesian radius $R=a$. So the center of the ring singularity in cartesian ...
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1answer
154 views

Quadrupole moment of Kerr spacetime

In this paper this paper, the Kerr black hole is described as having quadrupole moment of $q=J^2/M$ (which means $q=a^2M$ using $J=aM$) whereas in this paper it says in the abstract that the limiting ...
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For a given mass, how big can a Kerr black hole get?

We know that in a Kerr Black Hole the singularity is in the form of a 1 dimensional ring. If we have a 25 solar mass black hole, how big would the Kerr Ring be, width wise? Also, I read the Wiki on ...
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Can anyone tell me how can draw shadow of black hole like in presented in Intersteller movie? Is there any code for it in Mathematica or in Python? [closed]

Equation of motion for photon $$ \Sigma \frac{dt}{d\lambda} = aL\left(1-\frac{r^2+a^2}{\Delta}\right) + \omega\left(\frac{\left(r^2+a^2\right)^2}{\Delta}-a^2 \sin ^2\theta\right)\ , $$ $$ \Sigma\frac{...
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Gravitational lensing redshift around a Kerr black hole

Light from a source passes by a Kerr black hole on two sides at the equator and converges at the observer. The axis of rotation of the black hole is perpendicular to the direction of light. Two rays ...
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Is a stable orbit possible inside the ergosphere of a Kerr (spinning) black hole?

I have heard that it's "impossible to hover" inside of an ergosphere, but everywhere I read this seemed to be speaking in the context of "relative to a stationary observer outside of the ergosphere". ...
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Visualization of $ dtdx$ and $dxdy$ term in metric tensor

For the sake of simplicity, lets take a 2+1 dimensional spacetime. Lets take the metric $$ds^2 = g_{tt}dt^2 + g_{xx}dx^2 + g_{yy}dy^2 + g_{tx}dtdx + g_{xy}dxdy$$ What is the visualization or ...
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Centrifugal force on spinning black hole?

I saw the term spinning black hole popping up everywhere so my question do spinning black hole behave similarly to say a planet where it bulge in the equatorial and compress at the poles? what ...
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Kerr Black hole EH and Ergosphere embedding

Goodmorning everyone. I would like to share with you a question that has been gripping me for some time, but which I have never been able to give a convincing answer. When representing the ergosphere ...
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106 views

What would happen to the Earth, if the moon was a black hole? [closed]

Would it be a feasible scenario? I have read this question: What would happen to the Moon if Earth is turned into a black hole? Where Lubos Motl says: The extremal Kerr J=GM2/c∼RbhMc. Now, the ...
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Periodicity trick for Kerr Black Holes

I am slightly confused concerning the euclidean section of a Kerr black hole. In page 5 of the following paper https://arxiv.org/abs/hep-th/9908022 it is said that in order to get the euclidean ...
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Proof that the Kerr metric may be written in orthogonal form

Prove or disprove that the Kerr metric can be expressed in a set of orthogonal coordinates over some coordinate chart. Motivation for this question stems from my understanding that a metric can ...
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102 views

Kerr metric in BMS (Bondi-Metzner-Sachs) coordinates

I am trying to put the Kerr metric into the famous Bondi gauge, which is given for instance by the formula (6.2.10) at page 154 of the following paper: https://arxiv.org/abs/1801.01714. Now, Barnich ...